ATLANTA -- Delta Air Lines , facing a federal racial-discrimination complaint filed by part of the same legal team that hit Coca-Cola Co. with a high-profile race lawsuit, created a new executive position to promote global diversity.

Byron Perkins, a Birmingham, Ala., attorney who is co-counsel on the Coke suit, said he filed charges with the Equal Employment Opportunity Commission in Atlanta in early July on behalf of five African-American women who hold administrative and professional posts at Delta. The EEOC complaint,...